European Journal of Mechanics A-Solids最新文献

The work presented here proposes a contribution on the analysis of brake squeal phenomenon using a transient coupled finite element-discrete element method (FEM-DEM) simulation with pad surface topography evolution. To build the coupled FEM-DEM model, a non-overlapping strong coupling is first employed between the FEM and DEM subdomains. Second, a new calibration methodology of the DEM microscopic properties is proposed based on the eigenvalue analysis of the full model. The results of the coupled FEM-DEM model show a good agreement in terms of unstable frequencies and the evolution of the pad contact state history when compared to full FEM models, both for new and worn pad topographies. The evolution of the pad surface topography during the transient analysis results in a complex frequency behaviour, with abrupt shifts of instabilities and new operating deflection shapes, in agreement with reported experimental results. The proposed coupled FEM-DEM model thus seems to be a valuable tool for a better understanding of the squeal triggering due to the evolution of the pad surface topography. This contribution paves the way to advanced numerical analyses of brake squeal phenomenon, which triggering conditions are still under investigation.

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified general model. The ability of this general model to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the general model’s constitutive equations.

The current investigation explores the behavior of pre-stressed viscoelastic Timoshenko nanobeams under the influence of surface effects and a longitudinal magnetic field. Utilizing a modified version of non-local strain gradient theory through the Kelvin–Voigt viscoelastic model, a closed-form dispersion relation using a suitable analytical approach has been derived. To account for surface stresses, Gurtin–Murdouch surface elasticity theory has been employed. Additionally, the study delves into the impact of a longitudinal magnetic field on a single-walled carbon nanotube, considering Lorentz magnetic forces. The validity of the findings is established by deriving results in the absence of surface effects and magnetic fields, aligning well with existing literature. The investigation indicates that pre-stress has marginal effects on flexural and shear waves, while surface effects, magnetic fields, non-locality, characteristic length, and nanotube diameter significantly influence the phase velocity. Additionally, the threshold velocity and blocking diameter are discussed for the model.

The paper studies a penny-shaped crack in an infinite three-dimensional body of two-dimensional hexagonal quasicrystal media with piezoelectric effect. The crack surfaces are applied combined electric and normal phonon loadings. Such a Model I crack problem is transformed into a mixed boundary value problem in the upper half-space, which is analytically solved using Fabrikant's potential theory method. The boundary integral-differential equations governing Model I crack problems are presented for two-dimensional hexagonal piezoelectric quasicrystals. The normal phonon displacement discontinuity and electric potential discontinuity across crack surfaces are taken as the unknown variables of boundary governing equations. Analytical solutions of all field variables are derived not only for the crack plane but also for the full space. Solutions in integral form are provided for the penny-shaped crack under arbitrarily distributed electric and normal phonon loadings. Closed-form solutions in terms of elementary functions are given for concentrated point loadings and uniformly distributed loadings, respectively. Key fracture mechanics parameters, such as crack surface extended displacements (i.e., normal phonon displacement, electric potential), crack tip extended stresses (i.e., normal phonon stress, electric displacement) distribution, and corresponding extended stress intensity factors, are clearly derived. Numerical results are utilized to verify the present analytical solutions and graphically illustrate the distribution of phonon-phason-electric coupling fields around the crack. The present solution can serve as a benchmark for both experimental and numerical investigations.

The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.

The static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates (MGEKLPs), which incorporate two length-scale parameters related to strain gradient and rotation gradient effects, are comprehensively analyzed under various load forms and boundary conditions (BCs). The study of static stability employs static balance method and an improved energy method by introducing higher-order deformation gradients and corresponding energy terms. Utilizing the variational method, a sixth-order fundamental buckling differential equation for MGEKLPs under both transverse and in-plane loads is derived, serving as the foundation for the static balance method. The static stability analysis of MGEKLPs examines the combined effects of strain and rotation gradients on size-dependent critical buckling loads. Building on generalized strain energy with higher-order deformation energy, the energy method of classical elastic thin plate model is enhanced and applied to the static stability analysis of MGEKLPs. This approach enables the investigation of static stability without being constrained by the need to solve complex differential equations, making it applicable to various BCs and load scenarios. While static stability provides a description of stable state of an elastic system, dynamic stability offers a more scientific and rigorous analysis. The dynamic stability of simplified gradient elastic Kirchhoff–Love plates (SGEKLPs) with curved edges and different BCs is further investigated by combining the generalized strain energy with Lyapunov’s second stability method, presenting the dynamic stability criterion in the form of norms. A strict description of the dynamic stability of a SGEKLP over the entire time domain is provided for different supporting conditions, including case where all edges are supported and case with free edges. The analysis of size-dependent static and dynamic stabilities offers theoretical guidance for designing elastic thin plates with microstructures.

Unshearable and inextensible planar beams, in a static regime of finite displacements, are studied in this paper. A nonlinear mixed model is derived via a direct approach, in which displacements and reactive internal forces are taken as unknowns. The elasto-static problem is then addressed, and the role of the boundary conditions is systematically discussed. The relevant solutions for selected classes of problems are pursued via a perturbation method. It is shown that each considered class calls for a specific algorithm, accounting for a proper scaling and expansion of the variables. Finally, the asymptotic solutions are compared with benchmark numerical computations, grounded on finite-element analyses. The paper is focused on the case of longitudinal force significantly smaller than the buckling load, leaving the case of large force to future developments, where a different perturbation scheme is required.

In this study, a multiple-input multiple-output decoupling control (MIMO-DC) strategy is proposed based on the linear active disturbance rejection control (LADRC) algorithm to suppress the multi-modal vibration of flexible beams. Firstly, the dynamic equation of flexible beams is established using the Euler-Bernoulli beam theory. Then, a virtual control vector is introduced to decouple the MIMO system. The effectiveness of the flexible beam model is verified by comparing it with the experimental frequency response. Finally, experimental studies are carried out to analyze the vibration suppression performance of three control forms in suppressing the vibration of flexible beams under first-order modal excitation, second-order modal excitation, multi-modal excitation, variable multi-modal excitation, and multi-modal excitation with random disturbance, respectively. The robustness of the MIMO-DC strategy against parameter perturbations is also studied. The results show that the proposed MIMO-DC strategy not only exhibits excellent control performance for various types of modal excitations but also has strong adaptability to variable multi-modal excitation and strong anti-disturbance ability. Furthermore, the strategy exhibits strong robustness against parameter perturbations.

The paper presents a full-field crystal-plasticity computational investigation of $10\mu \epsilon$ small-strain-offset yield surfaces with pointed vertexes that are seen in the elastoplastic transition of pre-strained polycrystal metals. It is concluded that the shape of these yield surfaces obtained with a full-field spectral solver compares reasonably well with calculated ones by a simple aggregate Taylor model. The influence of material strength, work hardening, and texture are discussed. An assessment is made of the origin of anelasticity and Bauschinger effects at small strains, considering two mechanisms. Firstly, there is a built-in composite effect in crystal elastoplastic simulations due to the mixture of elastically and plastically loaded grains. Secondly, kinematic hardening of reverse slip systems will contribute to the Bauschinger effect. Based on analyses of the computed selected cases and comparison to previously published measurements, it is concluded that both mechanisms are important.

This work addresses differences in predicted elastic fields created by dislocations either by the Phase Field Crystal (PFC) model, or by static Field Dislocation Mechanics (FDM). The PFC order parameter describes the topological content of the lattice, but it fails to correctly capture the elastic distortion. In contrast, static FDM correctly captures the latter but requires input about defect cores. The case of a dislocation dipole in two dimensional, isotropic, elastic medium is studied, and a weak coupling is introduced between the two models. The PFC model produces compact and stable dislocation cores, free of any singularity, i.e., diffuse. The PFC predicted dislocation density field (a measure of the topological defect content) is used as the source (input) for the static FDM problem. This coupling allows a critical analysis of the relative role played by configurational (from PFC) and elastic (from static FDM) fields in the theory, and of the consequences of the lack of elastic relaxation in the diffusive evolution of the PFC order parameter.